Function to graph

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Function to graph

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

function to create the matrix

matrix creation X Y φ m X rows : n Y rows : 12 mat i 1 m range φ i 1 el Y i el : for j 2 n range i j m range φ i j el X j 1 - el X i el - φ j 1 - j 1 - el φ i j 1 - el - / : break try for for φ φ : 41 line :

Thiele Function

Thiele Function φ P p T size φ cols : i 1 size range s i el φ i i el : for i size 2 range i size ≡ T s i 1 - el p P i 1 - el - s i el eval / (+ : T T : 21 line T s i 1 - el p P i 1 - el - T / (+ : T T : 21 line if for φ P p T T : 41 line :

All Data X Xk 5 - 2 - 16 - 67 - 2781 mat :

All Data Y Yk 14621 / 72 / 077794 / 915118 / (- 1256131 / (31 - (14 / 48253 / (- 81 mat :

Given the following Table, obtain the Rational Function resulting from the Thiele algorithm

The equation in continuous fractions is:

Matrix with all the Data φ1 Xk Yk φ :

φ1 6.952 0.000 0.000 0.000 0.000 0.000 3.500 0.8690 - 0.000 0.000 0.000 0.000 0.000 0.8630 - 504.0 0.000 0.000 0.000 8.266 0.7613 - 37.15 - 0.01293 0.000 0.000 7.754 - 0.7480 - 66.11 0.01142 - 492.8 - 0.000 9.588 0.7589 - 45.43 - 0.01456 615.4 - 0.1060 2.214 - 0.7636 - 37.98 0.002146 - 530.5 - 0.1060 9.094 - 0.7478 - 74.29 0.01396 - 483.3 - 0.1060 86 mat

Thiele function with all the data φ1 Xk x T 14621 / x 5 - (- 126145 / - x 2 - (- 1058521 / x 1 - 48237265 / x 6 - (- 53713109 / - x 6 - 0.106031128404669 / + / + / + / + / +

DATA Xk Yk augment :

data DATA o 15 red plot :

x f φ1 Xk x T :

data x f 2 1 sys

The Thiele function goes through all the points, but it is overfitting

X data for training Xk1 5 - 2731 mat :

Y data for training Yk1 14621 / 31 - (14 / 48253 / (- 31 mat :

All Data X Xk 5.000 - 2.000 - 1.000 6.000 - 6.000 7.000 - 2.000 7.000 81 mat

All Data Y Yk 146.0 21.00 / 7.000 2.000 / 0.000 777.0 94.00 / 915.0 118.0 / - 1256 131.0 / 31.00 14.00 / - 482.0 53.00 / - 81 mat

Matrix with Training Data φ2 Xk1 Yk1 φ :

φ2 14621 / 003114 / - 4255 / - 048253 / - 33394465 / - 245575777 / 33 mat

Thiele function for training φ2 Xk x T 14621 / x 5 - (- 4255 / - x 2 - (- 316.055341055341 / + / +

x f φ1 Xk x T :

x f1 φ2 Xk x T :

Data for Test

Prediction by f1 (x)

Prediction by f (x)

X.pro 1.25 - 1.2 - 0 0.1 0.5 51 mat :

j 1 X.pro rows range :

Yf1.pro j el X.pro j el f1 : 2.0264 1.9596 0.3501 0.2152 0.3254 - 51 mat

Yf.pro j el X.pro j el f : 21.00 42.90 - 1.500 - 1.851 - 14.00 - 51 mat

DATA1 Xk1 Yk1 augment :

DATA2 X.pro Yf1.pro augment :

DATA3 X.pro Yf.pro augment :

data1 DATA1 o 25 black plot :

data2 DATA2 * 15 green plot :

data3 DATA3 X 8 red plot :

data4 16 augment'*-GOOD PREDICTION' 15 green plot :

data5 140 - augment'X-BAD PREDICTION' 15 red plot :

data data1 data2 data3 data4 data5 x f1 7 1 sys

The Thiele function with 3 points produces a line, which predicts better for the range -2 <x <1